This character is a Nonspacing Mark and inherits its script property from the preceding character. It is also used in the scripts Arabic, Syriac.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Nonspacing Mark. When changing direction it is not mirrored. U+0670 prohibits a line break before it. The glyph can be confused with 13 other glyphs.
The Wikipedia has the following information about this codepoint:
The dagger alif (Arabic: ألف خنجريةalif khanjarīyah) or superscript alif is written as a short vertical stroke on top of an Arabic letter. It indicates a long /aː/ sound where alif is normally not written, e.g. هَٰذَاhādhā or رَحْمَٰنraḥmān. The dagger alif occurs in only a few modern words, but these include some common ones; it is seldom written, however, even in fully vocalised texts, except in the Qur'an. As Wright notes "[alif] was at first more rarely marked than the other long vowels, and hence it happens that, at a later period, after the invention of the vowel-points, it was indicated in some very common words merely by a fatḥa [i.e. the dagger alif.]" Most keyboards do not have dagger alif. The word الله (Allāh) is usually produced automatically by entering "alif lām lām hāʾ", or in Arabic: "ا ل ل ه". The word consists of alif + ligature of doubled lām with a shadda and a dagger alif above lām.